Axial/equatorial — Organic Chemistry Notes

Draw methylcyclohexane as a chair and you have to decide where the methyl goes. Each ring carbon offers two positions, and they are not alike: one points straight up or down, and the other points out from the ring. The choice changes the molecule's energy by an amount you can measure. This section shows how to find both positions on a chair drawing, why one of them costs energy, and how to put a number on that cost. It builds on the chair from Cyclohexanes.

Two positions per carbon

Start with cyclohexane itself. Each of its six carbons bonds to two ring carbons and to two hydrogens, so a chair carries twelve hydrogens. They fall into two sets of six.

An axial bond points straight up or straight down. It runs parallel to the ring's axis, the imaginary line through the ring's center, at right angles to the ring. An equatorial bond points outward around the rim of the ring, its "equator," and tilts slightly up or down.

The axial bonds alternate as you go round the ring. If C1's axial bond points up, C2's points down, C3's points up, and so on. So C1, C3 and C5 have their axial bonds on the top face of the ring, and C2, C4 and C6 have theirs on the bottom face.

All twelve positions on one chair, with the carbons numbered C1 to C6.

Each carbon's equatorial bond tilts the opposite way from its own axial bond. On C1 the axial bond points up, so the equatorial bond angles slightly down. On C2 it is the reverse: the axial bond points down and the equatorial bond angles slightly up.

Two habits make a chair drawing come out right. Draw every axial bond exactly vertical, alternating in direction. Then draw each equatorial bond parallel to the ring bonds one carbon along: C1's equatorial bond runs parallel to the C2–C3 and C5–C6 bonds, and the same rule holds on every carbon.

1,3-diaxial interactions

Now put a methyl group on C1 in the axial position, pointing up. The axial bonds on C3 and C5 point up as well, and each carries a hydrogen. All three axial groups rise from the top face, close enough to crowd each other. That steric clash is a 1,3-diaxial interaction: steric strain between two axial groups on the same face, two carbons apart. (C5 is also two carbons from C1, counting the other way round.) An axial methyl has two of them, one with the axial hydrogen on C3 and one with the axial hydrogen on C5.

The same compound, methylcyclohexane, in two chair shapes. Only the hydrogens that matter are drawn, and dashed lines mark the contacts.

Put the methyl in the equatorial position instead and it points out, away from the ring. Nothing else on the ring reaches into that space, so an equatorial methyl has no 1,3-diaxial interactions. C1's axial position now holds a hydrogen, and its small contacts with the axial hydrogens on C3 and C5 are ones plain cyclohexane has too.

Each 1,3-diaxial contact between a methyl and a hydrogen costs about 0.9 kcal/mol. That is the same cost as one gauche interaction in butane, met in Newman projections. A Newman projection down a ring bond shows why. Sight down the C1–C2 bond. An axial methyl on C1 sits 60° from C3, the ring carbon bonded to the back carbon C2, just as the two methyls of gauche butane sit 60° apart. An equatorial methyl sits 180° from C3, which is the anti arrangement.

Both chairs of methylcyclohexane viewed down the C1–C2 bond, with C1 in front. Compare where the methyl sits relative to C3.

The C1–C6 bond gives the same picture with C5, so an axial methyl carries two gauche interactions, about 2 × 0.9 = 1.8 kcal/mol. In butane the central bond can turn the two methyls apart until they are anti. In a chair, the ring stops the C1–C2 and C1–C6 bonds from turning that far, so as long as the ring stays in this chair, an axial methyl stays gauche to C3 and C5.

A-values: putting a number on it

Methylcyclohexane can take either chair shape drawn above, with the methyl axial or with the methyl equatorial. The ring gets from one chair to the other only by turning about its C–C bonds, passing through the half-chair and twist-boat shapes from Cyclohexanes, and no bond breaks on the way. So the two chairs are two conformations of one compound, as Newman projections defined the word. Like the anti and gauche conformations of butane, both are present at once, and the lower-energy one is the more common.

Looking ahead: the next section, Ring flips, follows that path step by step and shows what happens to each bond as the ring turns.

The equatorial chair is lower in energy by 1.7 kcal/mol, close to the 1.8 that the two gauche interactions predict. At room temperature that gap puts about 95% of the molecules in the equatorial chair.

The A-value of a group is that energy gap: how much lower in energy, in kcal/mol, the chair with the group equatorial is than the chair with the group axial. A-values are measured, and each one converts directly into an equilibrium ratio.

Common A-values, smallest to largest, with the share of molecules that have the group equatorial.

The chart shows first that an A-value follows a group's width, not its mass. Chlorine is more than twice as heavy as a methyl group, yet its A-value is less than a third as large: 0.5 against 1.7. A chlorine atom sits at the end of a long C–Cl bond and presents a smooth sphere to the ring, while a methyl group fans three hydrogens out sideways.

The chart also shows a large jump from isopropyl (2.2) to tert-butyl (4.9). An axial isopropyl group can turn so that its one C–H bond points in over the ring, toward the axial hydrogens, and its two methyls point away. A tert-butyl group has no C–H bond on that carbon, so whichever way it turns, a methyl points at the axial hydrogens.

Worked example — turning an A-value into a ratio

An energy gap and an equilibrium ratio carry the same information. The equation that converts one into the other is ΔG = −RT ln K, or K = e^−ΔG/RT run the other way. Here K is the ratio of equatorial to axial molecules, and ΔG is the energy change on going from the axial chair to the equatorial chair, which is minus the A-value.

R is the gas constant and T the absolute temperature. At 298 K their product RT is about 0.59 kcal/mol, and that one number is all you need to carry. Because K depends exponentially on ΔG, each extra 0.59 kcal/mol multiplies the ratio by e, about 2.7.

For methylcyclohexane the A-value is 1.7 kcal/mol, so K = e^1.7/0.59 ≈ 18. The equilibrium is about 18:1 in favor of the equatorial chair, or roughly 95:5.

For tert-butylcyclohexane the A-value is 4.9 kcal/mol, so K = e^4.9/0.59 ≈ 4000, which is better than 99.97% equatorial. The energy gap is about three times larger, but the ratio is more than two hundred times larger, because the relationship is exponential.

A tert-butyl group is so strongly equatorial, over 99.9%, that chemists use it as a conformational anchor. The chair with the tert-butyl axial still exists, but it is too rare to matter, so the group in effect holds the ring in one chair. A chemist can then study a single, known conformation instead of a mixture of two. Much of what is known about how axial and equatorial groups react differently was measured this way.

Cis and trans on a ring

Two groups on a ring are cis when they sit on the same face and trans when they sit on opposite faces, as Rings & unsaturation showed. A flat hexagon shows the face with the solid and dashed wedges from Molecular geometry: a solid wedge comes up out of the page toward you, and a dashed wedge goes down behind it. Two solid wedges, or two dashed ones, is cis; one of each is trans.

Left: the flat drawings of the two isomers. Right: one chair, with the bond that points up on C1 and on C2 drawn bold.

Cis or trans is a fact about the compound, not about the drawing or the conformation. Turning the whole molecule over swaps up and down for every group at once, but it cannot change whether two groups share a face. Moving one group to the other face would mean breaking a bond and making a new one. So a cis ring and a trans ring are two different compounds that can be separated and bottled, while the two chairs of methylcyclohexane are one compound. Stereochemistry names these arrangements in full later; the up/down reading is all this chapter needs.

Now look at the chair in the figure. A group on the top face of C1 sits on C1's axial bond, because that bond points up. Next door, C2's axial bond points down, so a group on the top face of C2 has to use the equatorial bond. On neighboring carbons, the up bonds are always of different kinds.

"Up" and "axial" are not the same thing. Up or down tells you which face of the ring a group is on, and whether two groups share a face is fixed for the compound. Axial or equatorial tells you which kind of bond the group sits on in one particular chair. A group that points up may be axial or equatorial, depending on which carbon it is on.

Common questions

What is the difference between axial and equatorial bonds? Axial bonds are the vertical ones, parallel to the ring's axis; equatorial bonds run out sideways from the ring. Every ring carbon has one of each, giving a cyclohexane chair six axial and six equatorial positions.

Does an equatorial bond point up or down? Look at the axial bond on the same carbon first: the equatorial bond always leans the other way. An up axial bond means a slightly down equatorial bond, and vice versa.

Why do groups prefer the equatorial position? An axial group crowds the axial hydrogens two carbons away, the 1,3-diaxial interactions, while an equatorial group has none. For methylcyclohexane the equatorial chair is lower in energy by 1.7 kcal/mol, which puts about 95% of the molecules in that chair at room temperature.

What carries forward

Axial and equatorial are the vocabulary for the rest of this chapter. Conformational analysis, two sections on, uses A-values to decide which chair wins when a ring carries more than one group, and shows when one group has to sit axial in both chairs.

Looking ahead: size is not the only factor. On a sugar ring, an electronegative group on the carbon next to the ring oxygen often prefers the axial position for electronic reasons. This is the anomeric effect, which Biomolecules covers. When you meet it, the A-value table is not wrong; a second effect is at work.

Looking ahead: in Substitution & Elimination you will meet E2 elimination, a reaction that removes a hydrogen from one carbon and a group called the leaving group from the carbon next to it. On a ring it works only when the leaving group and a hydrogen on the next carbon are both axial, on opposite faces. It is the clearest case of a conformation deciding whether a reaction happens at all.